Merge branch 'development'

Author: aalhour

Algorithms/Algorithms.csproj

@@ -37,6 +37,7 @@
     <Compile Include="Graphs\DijkstraShortestPaths.cs" />
     <Compile Include="Numeric\BinomialCoefficients.cs" />
     <Compile Include="Numeric\CatalanNumbers.cs" />
+    <Compile Include="Numeric\GreatestCommonDivisor.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
     <Compile Include="Sorting\BinarySearchTreeSorter.cs" />
     <Compile Include="Sorting\BubbleSorter.cs" />

Algorithms/Numeric/GreatestCommonDivisor.cs

@@ -0,0 +1,44 @@
+/***
+ * Euclidean Algorithm to find the greatest common divisor of two numbers.
+ * 
+ */
+
+
+namespace Algorithms.Numeric
+{
+    public static class GreatestCommonDivisor
+    {
+        /// <summary>
+        /// Finds and returns the greatest common divisor of two numbers
+        /// </summary>
+        public static uint FindGCD(uint a, uint b)
+        {
+            if (a == 0)
+                return b;
+            else if (b == 0)
+                return a;
+
+            uint _a = a, _b = b;
+
+            uint q = _a / _b;
+            uint r = _a % _b;
+
+            while(r != 0)
+            {
+                _a = _b;
+                _b = r;
+                r = _a % _b;
+            }
+
+            return _b;
+        }
+
+        /// <summary>
+        /// Determines given two numbers are relatively prime
+        /// </summary>
+        public static bool IsRelativelyPrime(uint a, uint b)
+        {
+            return FindGCD(a, b) == 1;
+        }
+    }
+}

MainProgram/AlgorithmsTests/GreatestCommonDivisorTest.cs

@@ -0,0 +1,74 @@
+using System;
+
+using Algorithms.Numeric;
+
+
+namespace C_Sharp_Algorithms.AlgorithmsTests
+{
+    public static class GreatestCommonDivisorTest
+    {
+
+        public static void DoTest()
+        {
+            uint[,] testNumbers = new uint[8, 2]
+            {
+                {0,0 },
+                {0,5 },
+                {2,4 },
+                {3,10 },
+                {13,17 },
+                {12,20 },
+                {22,11 },
+                {33,22 }
+            };
+
+            for (int i = 0; i < testNumbers.GetLength(0); i++)
+            {
+                uint gcd = GreatestCommonDivisor.FindGCD(testNumbers[i, 0], testNumbers[i, 1]);
+
+                if (Assert(testNumbers[i,0], testNumbers[i,1], gcd))
+                {
+                    Console.WriteLine("{0,5}-{1,-5}: with gcd: {2,-5} : Success", testNumbers[i, 0], testNumbers[i, 1], gcd);
+                }
+                else
+                {
+                    Console.WriteLine("{0,5}-{1,-5}: with gcd: {2,-5} : Error", testNumbers[i, 0], testNumbers[i, 1], gcd);
+                }
+            }
+        }
+
+        private static bool Assert(uint a, uint b, uint gcdCandidate)
+        {
+            if (a == 0)
+                return b == gcdCandidate;
+            else if (b == 0)
+                return a == gcdCandidate;
+
+            if (a % gcdCandidate != 0 || b % gcdCandidate != 0)
+                return false;
+
+            //Suppose that gcdCandidate is not gcd.
+            //With this assumption, if gcdCandidate divides both a and b then it must divide the real gcd
+            //Namely, there should be a positive integer
+            uint q;
+            //such that gcd = q*gcdCandidate
+
+            q = 2;
+
+            uint _gcd = gcdCandidate * q;
+
+            while(_gcd < a && _gcd < b)
+            {
+                if (a % _gcd == 0 && b % _gcd == 0)
+                    return false;
+                
+                _gcd *= ++q;
+            }
+
+            return a > b ? 
+                ((a % b == 0) && (b == gcdCandidate)) || ((a % b != 0) && (b != gcdCandidate)) : 
+                ((b % a == 0) && (a == gcdCandidate)) || ((b % a != 0) && (a != gcdCandidate));
+        }
+
+    }
+}

MainProgram/MainProgram.csproj

@@ -48,6 +48,7 @@
     <Compile Include="AlgorithmsTests\GraphsCyclesDetectorTests.cs" />
     <Compile Include="AlgorithmsTests\GraphsDijkstraShortestPathsTest.cs" />
     <Compile Include="AlgorithmsTests\GraphsTopologicalSorterTest.cs" />
+    <Compile Include="AlgorithmsTests\GreatestCommonDivisorTest.cs" />
     <Compile Include="AlgorithmsTests\HeapSorterTest.cs" />
     <Compile Include="AlgorithmsTests\LSDRadixSorterTest.cs" />
     <Compile Include="AlgorithmsTests\StringEditDistanceTest.cs" />

README.md

@@ -119,6 +119,7 @@ Note: The projects where tested on Xamarin Studio (MonoDevelop) on OSX 10, and V
 
 #### Numeric:
  * [Catalan Numbers](Algorithms/Numeric/CatalanNumbers.cs).
+ * [Greatest Common Divisor](Algorithms/Numeric/GreatestCommonDivisor.cs)
 
 #### Visualization:
  * [Tree Drawer](DataStructures/Trees/TreeDrawer.cs).